How to generate url in twig passing parameters?

Why not do this instead:

search:
  path: /search/{value}
  defaults: { _controller: MyAppBundle:Default:search}

public function searchAction(Request $request, $value){
        // Do something with $value...

It doesn't address the URL issue, but you can easily set the value parameter in your Twig file, and this is the standard way to do it in Symfony.

EDIT #2 - based on comment.

What I do is something like this:

{{ path('searchPet',{'petID': pet.getPetId}) }}

In the above case, searchPet is the route, petID is the parameter name, and pet.getPetId is my pet method; where pet is a Petition Entitiy that I've passed in to the Controller (which Twig renders); So I'm calling getPetId() which returns the Id of the Petition.

So if you render in Controller like this with param being the variable:

return $this->render('search.html.twig', array(
                'param' => 'test',
                ...
            ));

Then in Twig do this:

{{ path('search', {'value': param}) }}

Then URL will be in this case: /search/test

EDIT #3 - based on last comment.

Quote the value you want to send, so you want to send 'test', do this:

{{ path('search', {'value': 'test'}) }}

I tested this - it works.

Your Controller will be like:

    #[Route('/place_payment/{id}', name: 'place_payment', methods: ['GET', 'POST'])]
    public function addPayment(Request $request, Place $place, int $id): Response
        {
            $idPayment = (int) $request->query->get('idPayment');

And your TWIG will be like:

    {% for payment in existingPayments %}
       <a href="{{ path('user_place_payment', {'id': place.id, 'idPayment': payment.id }) }}">{{ payment.name }} - delete this payment method</a><br><br>
    {% endfor %} 
    {% for payment in missingPayments %}
        <a href="{{ path('user_place_payment', {'id': place.id, 'idPayment': payment.id }) }}">{{ payment.name }} - add this payment method</a><br><br>
    {% endfor %} 

So, you get URL like your_server/place_payment/103?idPayment=3